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Publication Number: FHWA-HRT-12-030
Date: August 2012

 

Estimation of Key PCC, Base, Subbase, and Pavement Engineering Properties From Routine Tests and Physical Characteristics

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CHAPTER 5. MODEL DEVELOPMENT (7)

Figure 141 through figure 143 show the sensitivity of this model to CMC, w/c ratio, and age, respectively. These trends are all reasonable. Figure 141 and figure 142 show the change in compressive strength at two ages, 28 days and 1 year, which are almost at the lower and upper bounds of ages included in this model. The plot in figure 143 can be considered a strength gain curve for typical unit weight and w/c ratios used in mix designs.

This graph shows the sensitivity of the short-term cylinder compressive strength model to the cementitious materials content (CMC). The x-axis shows CMC from 300 to 1,100 lb/yd3, and the y-axis shows the predicted compressive strength values from 3,000 to 11,000 psi. The sensitivity is shown for CMC ranges from 350 to 1,000 lb/yd3 for strength predictions at 28 days and 1 year. The 28-day strength is plotted using solid squares connected by a solid line, and the 1-year strength is plotted using solid diamonds connected by a solid line. The graph shows that with increasing CMC, the predicted compressive strength increases. The water/cement ratio is -0.4, and the unit weight is 145 lb/ft3.

Figure 141. Graph. Short-term cylinder compressive strength sensitivity to CMC.

This graph shows the sensitivity of the short-term cylinder compressive strength model to the water/cement (w/c) ratio. The x-axis shows the w/c ratio from 0 to 0.8, and the y-axis shows the predicted compressive strength values from 2,000 to 8,000 psi. The sensitivity is shown for w/c ratio ranges from 0.25 to 0.70 for strength predictions at 28 days and 1 year. The 28-day strength is plotted using solid squares connected by a solid line, and the 1-year strength is plotted using solid diamonds connected by a solid line. The graph shows that with increasing w/c ratio, the predicted compressive strength decreases. The cementitious materials content is 600 lb/yd3, and the unit weight is 145 lb/ft3.

Figure 142. Graph. Short-term cylinder compressive strength sensitivity to w/c ratio.

This graph shows the sensitivity of the short-term cylinder compressive strength model to the pavement age. The x-axis shows the age in from zero to 1 year, and the y-axis shows the predicted compressive strength values from 3,000 to 9,000 psi. The sensitivity is shown for pavement ages from zero to 1 year, and the data are plotted using solid squares connected by a solid line. The graph shows that as the pavement ages, the predicted compressive strength increases.

Figure 143. Graph. Short-term cylinder compressive strength sensitivity to age.

 

Compressive Strength Model 3: Short-Term Core Strength Model

The core strength data in the LTPP database were used for this model. While the materials and test ages are similar to the short-term cylinder strength model, the compressive strength of the cores is representative of the consolidation and quality of construction in the field. An initial comparison of core versus cylinder strengths was performed to determine if there was a significant difference in two strength values. Data were matched by section and age. Data were grouped in several age categories so that strength comparisons could be made at corresponding ages. Generally, each category up to 56 days was grouped for ages of ±3 days. For ages close to 6 months to 1 year, the results were grouped for ages ±30 days. The ages at which strength test results were common to both cores and cylinders were 14 days, 21 days, 28 days, 35 days, 41 days, and 1 year.

The comparison showed that there was no significant difference between strength values determined from core or cylinder tests. The paired t-test results shown in table 25 indicate that there is no significant difference between the two strengths (P < t-critical). Figure 144, which has a trend line forced to zero intercept, shows the same results. Note that a trend line with a non-zero intercept produces a higher R2 (0.67), which is consistent with the Pearson correlation value of 0.82 presented in table 25.

In the development of this model, parameters similar to the cylinder strength model were evaluated. In addition, the effect of curing was considered with greater attention. However, curing did not prove to be a significant variable. As this model attempts to predict the strength up to 1 year in age, the variable accounting for age was treated in a hierarchical fashion.

This graph shows an x-y scatter plot comparing core compressive strength data with cylinder compressive strength data for Specific Pavement Studies (SPS) sections. The x-axis shows core compressive strength from zero to 12,000 psi, and the y-axis shows cylinder compressive strength from zero to 12,000 psi. The data are plotted as solid diamonds. The graph also has a line of equality with 
a slope of 1. The plot shows that the data are comparable, and the points are concentrated along the line of equality. The data range from about 2,000 psi to marginally over 10,000 psi. The following equations are also presented in the graph: y equals 0.9988x and R-squared equals 0.6175.

Figure 144. Graph. Comparison of core and cylinder strengths for SPS sections.

 

Table 25. Paired t-test results for comparison of core and cylinder strengths in SPS data.

Parameter

Core

Cylinder

Mean

5345.3

5472.3

Variance

3,307,974.59

3,003,561.77

Observations

312

312

Pearson correlation

0.82

Hypothesized mean difference

0

DF

311

t-Stat

-2.11

P(Tt) one-tail

0.02

t-critical one-tail

1.65

P(Tt) two-tail

0.04

t-critical two-tail

1.97

 

This model was established as shown in figure 145.

f subscript c,t equals 98.92962 plus 5.70412 times CMC plus 28.48527 times uw plus 2,570.13151 times MAS times w/c minus 199.84664 times FM plus 611.30879 times natural log open parenthesis t closed parenthesis.

Figure 145. Equation. Prediction model 3 for fc,t.

Where:

fc,t = Compressive strength at age t years, psi.

CMC = Cementitious materials content, lb/yd3.

uw = Unit weight, lb/ft3.

MAS = Maximum aggregate size, inch.

w/c = Water to cementitious materials ratio.

FM = Fineness modulus of fine aggregate.

t = Short-term age in years.

The regression statistics for this model are presented in table 26. The model was developed using 294 points, and the prediction has an R2 value of 67.6 percent and an RMSE value of 1,122 psi. Table 27 provides details of the range of data used to develop the model. Figure 146 and figure 147 show the predicted versus measured plot and the residual plot, respectively. Figure 148through figure 153 show the sensitivity of this model to CMC, unit weight, MAS, w/c ratio, FM, and age, respectively.

 

Table 26. Regression statistics for short-term core strength model.

Variable

DF

Estimate

Standard Error

t-Value

Pr > |t|

VIF

Intercept

1

98.92962

1,544.34064

0.06

0.949

0

Cementitious

1

5.70412

0.36589

15.59

< 0.0001

1.23548

Unit weight

1

28.48527

10.59672

2.69

0.0076

1.0182

(MAS) × (w/c ratio)

1

2,570.13151

538.267

-4.77

< 0.0001

1.2201

Fineness modulus (FM)

1

-199.84664

120.68288

-1.66

0.0988

1.01426

Ln(age)

1

611.30879

45.08962

13.56

< 0.0001

1.00026

 

The model statistics for table 26 are as follows:

Table 27. Range of data used for short-term core strength model.

Parameter

Minimum

Maximum

Average

w/c ratio

0.27

0.69

0.42

Cementitious content

376

999

670

Unit weight

120

163

144

MAS

0.375

1.000

0.683

FM

2.50

4.37

3.05

Pavement age

0.0380

2.2160

0.4230

Compressive strength

1,990

11,350

5,596

 

This graph shows an x-y scatter plot of the predicted versus the measured values used in the short-term core compressive strength model. The x-axis shows the measured compressive strength from zero to 12,000 psi, and the y-axis shows the predicted compressive strength from zero to 12,000 psi. The plot contains 294 points, which correspond to the data points used in the model. The graph also shows a 45-degree line that represents the line of equality. The data are shown as solid diamonds, and they appear to demonstrate a good prediction. The measured values range from 1,990 to 11,350 psi. The graph also shows the model statistics as follows: N equals 294, R-squared equals 0.6761 percent, and root mean square error equals 1,122 psi.

Figure 146. Graph. Predicted versus measured for short-term core compressive strength model.

This graph is an x-y scatter plot showing the residual errors in the predictions of the short-term core compressive strength model. The x-axis shows the predicted compressive strength from zero to 10,000 psi, and the y-axis shows the residual compressive strength from -4,000 to 4,000 psi. The points are plotted as solid diamonds, and they appear to show no significant bias (i.e., the data are well distributed about the zero-error line). There appears to be no trend in the data, and the trend line is almost horizontal (i.e., zero slope). The following equations are also provided in the graph: y equals 2E minus 0.7x plus 0.0005 and R-squared equals 7E minus 14.

Figure 147. Graph. Residual errors for short-term core compressive strength model.

This graph shows the sensitivity of the short-term core compressive strength model to the cementitious materials content (CMC). The x-axis shows CMC from 300 to 1,100 lb/yd3, and the y-axis shows the predicted compressive strength from 3,000 to 11,000 psi. The sensitivity shown for CMC ranges from 350 to 1,000 lb/yd3 for strength predictions at 28 days and 1 year. The 28-day strength is plotted using solid squares connected by a solid line, and the 1-year strength is plotted using solid diamonds connected by a solid line. The graph shows that with increasing CMC, the predicted compressive strength increases. The water/cement ratio is 0.4, the unit weight is 
145 lb/ft3, the maximum aggregate size is 0.75 inches, and the fineness modulus is 3.0.

Figure 148. Graph. Short-term core compressive strength sensitivity to CMC.

This   graph shows the sensitivity of the short-term core compressive strength model to the unit weight. The x-axis shows the unit weight from 120 to 170 lb/ft3, and the y-axis shows the predicted compressive strength from 3,000 to 9,000 psi. The sensitivity shown for unit weight ranges from 125 to 155 lb/ft3 for strength predictions at 28 days and 1 year. The 28-day strength is plotted using solid squares connected by a solid line, and the 1-year strength is plotted using solid diamonds connected by a solid line. The graph shows that with increasing unit weight, the predicted compressive strength increases. Cementitious materials content equals 600 lb/yd3, the water/cement ratio equals 0.4, maximum aggregate size equals 0.75 inches, and fineness modulus equals 3.0.

Figure 149. Graph. Short-term core compressive strength sensitivity to unit weight.

This graph shows the sensitivity of the short-term core compressive strength model to the maximum aggregate size (MAS). The x-axis shows the maximum aggregate size from 0.2 to 1.2 inches, and the y-axis shows the predicted compressive strength from 3,000 to 9,000 psi. The sensitivity is shown for aggregate size ranges from 0.375 to 1 inch for strength predictions at 28 days and 
1 year. The 28-day strength is plotted using solid squares connected by a solid line, and the 
1-year strength is plotted using solid diamonds connected by a solid line. The graph shows that with increasing MAS, the predicted compressive strength decreases. Cementitious materials content equals 600 lb/yd3, the water/cement ratio equals 0.4, the unit weight equals 145 lb/ft3, and fineness modulus equals 3.0.

Figure 150. Graph. Short-term core compressive strength sensitivity to MAS.

This graph shows the sensitivity of the short-term core compressive strength model to the water/cement (w/c) ratio. The x-axis shows the w/c ratio from 0.2 to 0.8, and the y-axis shows the predicted compressive strength from 3,000 to 9,000 psi. The sensitivity is shown for w/c ratio ranges from 0.25 to 0.70 for strength predictions at 28 days and 1 year. The 28-day strength is plotted using solid squares connected by a solid line, and the 1-year strength is plotted using solid diamonds connected by a solid line. The graph shows that with increasing w/c ratio, the predicted compressive strength decreases. Cementitious materials content is 600 lb/yd3, the unit weight is 145 lb/ft3, maximum aggregate size is 0.75 inches, and fineness modulus is 3.0.

Figure 151. Graph. Short-term core compressive strength sensitivity to w/c ratio.

This graph shows the sensitivity of the short-term core compressive strength model to the fineness modulus (FM). The x-axis shows FM from 1 to 6, and the y-axis shows the predicted compressive strength from 3,000 to 9,000 psi. The sensitivity is shown for a FM range of 2 to 4.5, and the strengths are predicted at ages of 28 days and 1 year. The 28-day strength is plotted using solid squares connected by a solid line, and the 1-year strength is plotted using solid diamonds connected by a solid line. The graph shows that with increasing FM, the predicted compressive strength decreases. Cementitious materials content is 600 lb/yd3, the water/cement ratio is 0.4, the unit weight is 145 lb/ft3, and maximum aggregate size is 0.75 inches.

Figure 152. Graph. Short-term core compressive strength sensitivity to fine aggregate FM.

This graph shows the sensitivity of the short-term core compressive strength model to the pavement age. The x-axis shows the pavement age from zero to 1.4 years, and the y-axis shows the predicted compressive strength from 3,000 to 9,000 psi. The sensitivity is shown for pavement ages from zero to 1 year, and the data are plotted using solid squares connected by a solid line. The graph shows that as the pavement ages, the predicted compressive strength increases. Cementitious materials content is 600 lb/yd3, the water/cement ratio is 0.4, the unit weight is 145 lb/ft3, maximum aggregate size is 0.75 inches and fineness modulus is 3.0.

Figure 153. Graph. Short-term core compressive strength sensitivity to age.

 


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